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MathGroup Archive 1998

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RE: Re: Bug in Calculus`DiracDelta`

  • To: mathgroup at smc.vnet.net
  • Subject: [mg14847] RE: [mg14803] Re: Bug in Calculus`DiracDelta`
  • From: "Ersek, Ted R" <ErsekTR at navair.navy.mil>
  • Date: Fri, 20 Nov 1998 02:16:56 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

In the message below Martin Rommel wrote:
>
>
>If I had a too much time I would like to extend the DiracDelta>
>definition so that for the case of definite integrals the argument is
>checked for zeroes in the relevant interval and not "just somewhere".
>
>Of course, my original problem was not as trivial as the posted
>illustration.
>One more proof that you still have to know what you are doing and use
>Mathematica only for checking your analytical results.
>
>
I disagree.  I say you can use mathematica to come up with the analytical
results as long as you verify the results using independent methods (often
with Mathematica as well).

Ted Ersek

_____________________________

Well, I looked at the package Calculus`DiracDelta`. It looks like to
evaluate if the argument of DiracDelta has a zero Solve is used. In my
case that is

In[3]:=     Solve[Cos[phi]==0,x]

Solve::"ifun": "Inverse functions are being used by Solve, so some
solutions may not be found."

Out[3]=   {{phi ->-Pi/2}, {phi->Pi/2}}

There lies the problem, the solution {phi->3 Pi/2} is not considered. So
multivalued functions remain a potential pitfall, even if you limit
yourself (or Mathematica) to a safe interval. Unfortunately using
DiracDelta I do not get the warning!

If I had a too much time I would like to extend the DiracDelta
definition so that for the case of definite integrals the argument is
checked for zeroes in the relevant interval and not "just somewhere".

Of course, my original problem was not as trivial as the posted
illustration.
One more proof that you still have to know what you are doing and use
Mathematica only for checking your analytical results.

Thanks for your attention,

Martin.



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